Answer:
The standard deviation of the heights of the group of trees is 3 feet
Step-by-step explanation:
For a normal distribution, the z-score corresponding to a particular observed value is calculated as;
z-score = (observed value - mean) / (standard deviation)
The mean is given as 14.3
The z-score is 1.9
The observed value is 20 (the given height)
We can make the standard deviation to be the subject of the formula in the above equation;
standard deviation = (observed value - mean) / ( z-score)
We then substitute the given values into this equation;
standard deviation = ![\frac{20-14.3}{1.9}=3](https://tex.z-dn.net/?f=%5Cfrac%7B20-14.3%7D%7B1.9%7D%3D3)
Answer:
![(5x - 3y + 2)^2=25x^2+9y^2+4-30xy-12y+20x](https://tex.z-dn.net/?f=%285x%20-%203y%20%2B%202%29%5E2%3D25x%5E2%2B9y%5E2%2B4-30xy-12y%2B20x)
Step-by-step explanation:
We need to expand (5x – 3y + 2)² using identity.
Using identity,
![(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac](https://tex.z-dn.net/?f=%28a%2Bb%2Bc%29%5E2%3Da%5E2%2Bb%5E2%2Bc%5E2%2B2ab%2B2bc%2B2ac)
We have, a = 5x, b = -3y and c = 2
So,
![(5x - 3y + 2)^2=(5x)^2+(-3y)^2+2^2+2(5x)(-3y)+2(-3y)(2)+2(2)(5x)\\\\=25x^2+9y^2+4-30xy-12y+20x](https://tex.z-dn.net/?f=%285x%20-%203y%20%2B%202%29%5E2%3D%285x%29%5E2%2B%28-3y%29%5E2%2B2%5E2%2B2%285x%29%28-3y%29%2B2%28-3y%29%282%29%2B2%282%29%285x%29%5C%5C%5C%5C%3D25x%5E2%2B9y%5E2%2B4-30xy-12y%2B20x)
So, the required answer is
.
Answer:
-3 and 1
Step-by-step explanation:
-3 x 1 = -3
-3 + 1 = -2